ABSTRACT

Birds morph their wings during a single wingbeat, across flight speeds and among flight modes. Such morphing may allow them to maximize aerodynamic performance, but this assumption remains largely untested. We tested the aerodynamic performance of swept and extended wing postures of 13 raptor species in three families (Accipitridae, Falconidae and Strigidae) using a propeller model to emulate mid-downstroke of flapping during take-off and a wind tunnel to emulate gliding. Based on previous research, we hypothesized that (1) during flapping, wing posture would not affect maximum ratios of vertical and horizontal force coefficients (CV:CH), and that (2) extended wings would have higher maximum CV:CH when gliding. Contrary to each hypothesis, during flapping, extended wings had, on average, 31% higher maximum CV:CH ratios and 23% higher CV than swept wings across all biologically relevant attack angles (α), and, during gliding, maximum CV:CH ratios were similar for the two postures. Swept wings had 11% higher CV than extended wings in gliding flight, suggesting flow conditions around these flexed raptor wings may be different from those in previous studies of swifts (Apodidae). Phylogenetic affiliation was a poor predictor of wing performance, due in part to high intrafamilial variation. Mass was only significantly correlated with extended wing performance during gliding. We conclude that wing shape has a greater effect on force per unit wing area during flapping at low advance ratio, such as take-off, than during gliding.

INTRODUCTION

Flying birds use their wings to accomplish a diverse range of behaviors, including take-off and landing, maneuvering, cruising and soaring flight. Aerodynamic performance during each type of locomotion may be maximized by altering wing configuration, and birds often dynamically readjust their wing posture as they transition from one behavior to another or as they interact with varying aerodynamic conditions. In particular, birds partially retract their wings into a swept configuration during a variety of aerial behaviors. For example, birds sweep back their wings during upstroke in response to changing flight speeds and modulate wing flexion according to speed and glide angle (Pennycuick, 1968; Tucker, 1987; Tucker and Parrott, 1970). Swifts actively modify wing sweep to alter sink speed and turning rate during maneuvers (Lentink et al., 2007). Eagles sweep their wings back in response to turbulence (Reynolds et al., 2014). Dynamic (i.e. instantaneously variable) wing morphing appears to be ubiquitous among flying birds, and it is generally hypothesized that such morphing optimizes aerodynamic performance.

Although wing morphing is known to alter flight performance during high-speed gliding in ways that influence maneuvering (Lentink et al., 2007), the aerodynamic consequences of wing morphing at different flight speeds and between flapping and gliding are not well understood. As birds transition from slow to high speed, they continue to flap their wings. During this transition, the body velocity relative to wing-tip velocity increases. This relationship is called advance ratio (J):
(1)

where V is free-stream velocity (m s−1), Ω is angular velocity of the wing (rad s−1) and b is wing length (m). During hovering and very slow flight, such as immediately after take-off or before landing, J is zero and very low, respectively (Provini et al., 2012, 2014; Tobalske, 2007). J increases with increasing translational velocity of the whole bird, going to infinity during gliding. We tested the effects of swept and extended wing configurations on aerodynamic performance at low and high J.

Current understanding suggests that during flapping flight, subtleties of wing shape have little impact on aerodynamic performance (Usherwood and Ellington, 2002a, 2002b). Specifically, propeller models that emulate the mid-downstroke of flapping flight at low J reveal that aspect ratio (AR, wing span/average wing chord) has virtually no effect on aerodynamic force coefficients except at the highest angles of attack (α), which are probably not biologically relevant for birds (Usherwood and Ellington, 2002a,b). For gliding (J=∞), it has long-been assumed that selective pressures have promoted aerodynamic efficiency (i.e. lift:drag ratio) among flying animals (Allen, 1888; Averill, 1927; Beaufrère, 2009; Savile, 1957). The most efficient gliding birds are presumed to be those with either long, high-AR wings (e.g. frigatebirds and albatrosses) or emarginated, vertically separated primary feathers (e.g. hawks and vultures). These morphologies exhibit extended wings and increase span efficiency by minimizing induced drag caused by the wing-tip vortex (Henningsson et al., 2014; Spedding and McArthur, 2010). In both cases, these efficient wings minimize the effect of the wing-tip vortex by either (1) increasing AR and thereby reducing the strength of the wing-tip vortex (Viieru et al., 2006) or (2) dispersing and shedding the wing-tip vortex away from the upper surface of the wing in a manner similar to winglets on aircraft (Tucker, 1993, 1995).

Cumulatively, these studies led us to form two hypotheses. First, we hypothesized that at low J, both swept and extended wings should produce similar aerodynamic force coefficients (H1). Second, we hypothesized that at high J, extended wings (due to their increased span and slotted distal primary feathers) should have higher ratios of vertical to horizontal force coefficients (CV:CH) compared with swept wings (H2).

List of symbols and abbreviations

AR

aspect ratio

b

wing length (m)

CH

coefficient of horizontal force

CV

coefficient of vertical force

FH

horizontal force (N)

FV

vertical force (N)

J

advance ratio

Q

torque (N m) about the z-axis

Re

Reynolds number

S

wing area (m2)

S2

second moment of area of the wing (m4)

S3

third moment of area of the wing (m5)

V

free-stream velocity (m s−1)

α

angle of attack

ρ

air density

Ω

angular velocity of the wing (rad s−1)

To test these hypotheses, we studied wing performance in 13 raptor species (falcons, hawks and owls; Falconidae, Accipitridae and Strigidae) using a propeller model (see Usherwood, 2009; Heers et al., 2011), emulating wing translation during mid-downstroke at low J as in take-off or landing, and in a wind tunnel, emulating gliding when J=∞. The species in our sample had varying degrees of slotted distal wing planforms when their wings were extended as a result of emargination of their primary feathers. These birds routinely engage in take-off and landing (low J) and intermittent flight consisting of flapping phases interspersed with glides (high J). At low J, birds always flap their wings fully extended. Our study, however, allowed us to explore the aerodynamics associated with swept wings at low J, which could be useful in understanding why birds take off with fully extended wings and also in aiding the design of bird-like micro air vehicles. Furthermore, the natural variation in wing shape across the 13 species in this study allowed us to test for aerodynamic differences among clades and explore the evolutionary context of wing morphing.

MATERIALS AND METHODS

Specimens

We measured 26 wings from 13 species of raptors, a large, multiphyletic guild. These birds ranged in mass from 81 to 1860 g (Table 1). We gathered specimens that had already died from a variety of causes unrelated to this study, and many were missing organs or had become severely dehydrated. For this reason, some masses were estimated using averaged sex-specific values (Dunning, 1992) and are denoted with an asterisk in Table 1.

Wing preparation

We removed the wings from the bird at the shoulder between the humeral head and the glenoid cavity. We then positioned them in either an extended or a swept configuration (Fig. 1), pinned them on a foam board, and dried them at 50°C for 1–3 weeks until the connective tissue hardened. Extended angles were chosen based on the maximum the skeleton and connective tissues would allow, generally forming a straight leading edge. Swept angles were approximated at ∼40 deg, but often changed during drying as the connective tissue contracted. Post hoc sweep angles were measured between the humeral head, wrist joint and tip of the leading-edge primary feather, and are reported in Table 1. Once the wings had dried, we drilled into the head of the exposed humerus and inserted a brass tube (4–5 mm diameter) into the hollow bone matrix, cementing it in place using Devcon 5 Minute® epoxy. The brass tubes were counterbalanced internally so we could avoid oscillations associated with spinning unbalanced wings.

Swept and extended wings. Birds are capable of morphing their wings into a swept and extended configuration, resulting in reduced area, increased leading edge angle and reduction of wing-tip slots. Pictured here are the wings of a sharp-shinned hawk (Accipiter striatus).

We used a lateral view of the distal 1/3 of the wing to set the geometric angle of attack (α) prior to aerodynamically loading the wings, but considered the attack angle to be zero when lift was zero. Spanwise twist (i.e. washout) was a ubiquitous characteristic among the wings, and the wings deformed under aerodynamic load (Heers et al., 2011) causing the local α to vary greatly. To obtain an objective measure of zero-lift α for comparison among wings, we first interpolated our force values at 1 deg increments using a cubic spline between empirical measurements for α ranging from −5 deg<α<+50 deg. Then we adjusted our measured α to be zero when lift was 0 N.

When possible, we report differences between swept and extended wings using the following percentage change formula, where relevant values (e.g. CV or FV) are substituted:
(3)

Wind tunnel measurements

To explore the aerodynamics associated with high-J, translational flight, we used custom-designed wind tunnels at the Flight Laboratory at the University of Montana (Tobalske et al., 2005) and the Concord Field Station at Harvard University (Tobalske et al., 2003a). We sampled each wing at 8 m s−1. The wing was affixed with a brass rod to a NEMA 23 stepper motor (23W108D-LW8, Anaheim Automation, Inc., Anaheim, CA, USA) fastened to a force plate (see ‘Force measurements’, below, for details), located outside the tunnels. The wings were rotated through attack angles in 4.5 deg increments, controlled using an Arcus ACE-SDE controller (Arcus Technology, Inc., Livermore, CA, USA). We calculated Reynolds number (Re) by measuring the wing chord at the base of the alula feather. To test for effects of aeroelastic deformation at higher velocities, we tested a subset of the wings at 10 and 14.1 m s−1 and noted no difference in the vertical or horizontal coefficients. Those results are omitted here for simplicity.

Propeller measurements

We spun the wings like a propeller to emulate mid-downstroke during low-J flapping flight (Heers et al., 2011; Usherwood, 2009; Usherwood and Ellington, 2002a,b). We applied estimated in vivo angular velocities (Ω, rad s−1) using known wingbeat frequencies and stroke excursion angles from prior studies (Jackson and Dial, 2011; Tobalske and Dial, 2000). For birds <800 g in body mass, we used logΩ=0.01966logm+2.0391, and for birds >800 g, we used logΩ=0.3055logm+2.1811, where m is mass. The larger birds' wings broke when spun using the angular velocity equation of the smaller birds, necessitating the second equation fitted specifically to birds >800 g. We measured the vertical force and torque these wings generated using 5–10 deg increments in α. We ran several of the wings at various angular velocities and noted no significant difference in the resulting coefficients of aerodynamic force.

For birds <800 g, we used a NEMA 23 stepper motor (23W108D-LW8, Anaheim Automation, Inc.). For birds >800 g, we used a NEMA 34 stepper motor (34Y314S-LW8, Anaheim Automation, Inc.) coupled with a 3:1 planetary inline reduction gearbox (GBPH-060x-NP, Anaheim Automation, Inc.). The two motors were controlled using the same Arcus controller used in the wind tunnel measurements.

Force measurements

We measured aerodynamic forces using a custom-made force plate (15×15 cm platform, 200 Hz resonant frequency; Bertec Corporation, Columbus, OH, USA) for wings from birds <800 g, and a Kistler type-9286A force plate (Kistler Instruments Corp., Amherst, NY, USA) for wings from birds >800 g. At each α, we collected data at 1 kHz for several seconds and then filtered those force traces using a 3 Hz low-pass Butterworth filter before taking an average of the forces over the duration of the measurement. Raw force traces contained considerable noise due to aeroelastic flutter (Fig. 2).

For comparisons among wings, we non-dimensionalized the forces into vertical and horizontal coefficients using the following equations (see Usherwood and Ellington, 2002a):

flapping flight:
(4)gliding flight:
(5)

where CV is the coefficient of vertical force, CH is the coefficient of horizontal force, FV is vertical force (N), FH is horizontal force (N), Q is torque (N m) about the z-axis, ρ is air density at Missoula, MT, USA (978 m elevation, 1.07 kg m−3), or Bedford, MA, USA (41 m elevation, 1.204 kg m−3), Ω is angular velocity of the spinning wing (rad s−1), S is the area (m2), S2 is the second moment of area of the wing (m4) and S3 is the third moment of area of the wing (m5; Table S1).

Statistics and phylogenetic analysis

To test for effects of mass on peak CV:CH values, we used phylogenetically independent contrasts (PIC; see Felsenstein, 1985) computed using a consensus tree of our experimental species downloaded from birdtree.org (Jetz et al., 2012; Revell, 2012). We tested for effects at the family level using phylogenetic ANOVA (R Core Team 2015, http://www.R-project.org; Revell, 2012). We compared continuous variables using phylogenetically independent contrasts within linear models. We used paired t-tests to test for significant differences between swept and extended wings in peak force coefficients and absolute force. We report means±1 s.d.

RESULTS

Flapping coefficients

For the propeller model (emulating mid-downstroke of flapping at J=0), extended wings had significantly higher peak CV:CH than swept wings (P<0.0001, paired t-test; Fig. 3). On average, peak CV:CH was 3.7±0.8 for extended wings and 2.6±0.9 for swept wings, a 30.9% difference. Changes in CV were responsible for most differences in CV:CH between swept and extended wings (Figs 4 and 5). Swept-wing average peak CV was 23.1±32.3% lower than that of extended wings, and average peak CH was 2.0±59.4% lower. Differences between average swept and extended peak CV were statistically significant (P<0.004) and differences in average peak CH were nearly significant (P=0.08).

CV as a function of α in extended and swept postures during emulated flapping and gliding. The shaded regions represent ±s.d.

The angles at which average peak CV:CH occurred were α=17.5±2.8 deg for extended wings and α=22.3±9.2 deg for swept wings. The highest individual CV:CH recorded was 4.8 at α=18 deg for the extended flapping wing of the rough-legged hawk (Buteo lagopus). The red-tailed hawk (Buteo jamaicensis) had the highest swept CV of 1.2 at α=44 deg, while the rough-legged hawk exhibited the highest extended CV of 2.0 at α=43 deg (Table 2, Fig. 6; Table S2).

Individual polar plotsof CV as a function of CH for wings of 13 raptor species in different postures during flapping and gliding flight. Wings were configured in extended and swept postures and either spun as a propeller to emulate flapping flight or mounted in a wind tunnel to emulate gliding flight. For definitions of the four-letter abbreviations, see Table 1.

Gliding coefficients

During modeled gliding flight in the wind tunnel (where J=∞), peak swept and extended wing CV:CH ratios were not significantly different (P=0.5, paired t-test; Figs 3 and 4). The average peak CV:CH ratio for extended wings was 4.8±1.1 at α=13.1±2.1 deg, while the average for swept wings was 4.7±1.6 at α=12.6±1.9 deg, a difference of only 0.7%. Similar to flapping, CV mediated most of the differences in CV:CH. In gliding, the average peak CV of swept wings was 10.6±23.5% higher than that of extended wings, while the average peak CH was 2.8±14.8% lower (Figs 4 and 5).

The swept wing of the great horned owl (Bubo virgianus) had the highest individual peak CV:CH of 7.9 at α=11 deg. The peregrine falcon (Falco peregrinus) had the highest swept CV of 1.4 at α=38 deg, while the great-horned owl exhibited the highest extended CV of 1.4 at α=40 deg (Table 2, Fig. 6; Table S2).

Absolute forces

Absolute forces varied greatly as a result of differences in wing area (S), shape and, in the propeller model, angular velocity (Ω), second moment of area (S2) and third moment of area (S3). Swept wings had 26.6±10.3% less area, 57.9±14.4% lower S2 and 68.2±14.1% lower S3 than extended wings (Table S1).

During emulated flapping, swept wings produced 68.0±16.1% less peak FV and 68.9±22.0% less peak FH than extended wings. The percentage change between extended and swept wings for both peak FV and FH was not significantly different from that in S2 or S3 (P>0.1, paired t-test, for both). During emulated gliding, swept wings produced on average 20.6±12.8% less peak FV and 29.4±11.8% less peak FH than extended wings.

The extended wing of the great-horned owl produced the highest FV of all the wings tested during emulated gliding flight, 6.7 N (36.7% body weight per wing), at α=39 deg and 8 m s−1. The extended wing of this species produced 3.9 N (21.2% body weight per wing) during emulated flapping flight at α=44 deg and 15.2 rad s−1. During emulated flapping flight, the extended wing of the rough-legged hawk produced the highest vertical force, 4.4 N (54.0% body weight), at α=43 deg and 19.6 rad s−1. The American kestrel (Falco sparverius) wing produced the highest force as a percentage of body weight during modeled gliding flight at 66% (132% when considering two wings). The highest force relative to body weight observed on the propeller model came from the wing of the merlin (Falco columbarius); it supported 86.8% of body weight (167% for two wings). On average, individual extended wings produced 47% weight support during emulated gliding flight and 48% weight support during emulated flapping flight. In emulated gliding flight, the average critical attack angle was α=32±6 deg for swept wings and α=28±6 deg for extended wings, while in emulated flapping flight, the average critical attack angle was α=48±2 deg for swept wings and α=45±4 deg for extended wings.

Interspecific and morphological patterns

During emulated gliding, accipiter wings had the highest average peak CV:CH ratios in both swept and extended configurations (5.3±1.2 and 5.5±0.7, respectively). Conversely, falcons had the lowest average peak CV:CH ratios in swept and extended wing configurations during emulated gliding (3.3±0.4 and 3.8±0.8, respectively). Owl wings had average peak CV:CH ratios during emulated gliding of 4.9±2.0 for swept wings and 4.4±1.0 for extended wings. During emulated flapping, swept and extended accipiter wings similarly had the highest average peak CV:CH ratios (2.9±0.4 and 4.2±0.7, respectively). Falcon (1.8±0.6 and 3.4±0.4, swept and extended) and owl (2.6±1.2 and 3.2±0.7, swept and extended) wings had lower average peak CV:CH ratios during emulated flapping. Despite this variation, peak CV:CH between families was not significant for any wing posture or flight style (phylogenetic ANOVA, P>0.4 for all).

Summary of results of statistical tests (P-values) for significant effects of posture, flight style and morphology upon aerodynamic performance of wings of 13 species of raptors

DISCUSSION

Wing sweep differentially influenced aerodynamic performance on a per unit area basis (i.e. CV and CH). During emulated flapping, extended wings outperformed swept wings in both CV and CV:CH, whereas during emulated gliding, swept wings outperformed extended wings in CV and matched performance in CV:CH. These results provide insight into the relationship between wing posture and aerodynamic performance in raptors.

In emulated flapping flight, angular velocity of the rotating wing causes the wing tips to move more quickly than the wing roots. As aerodynamic forces vary with the square of local velocity, longer wings produce exponentially greater forces. Furthermore, local flow conditions (as indicated in the coefficients) likely change according to wing posture, and may influence aerodynamic forces. In flapping flight, extended wings had 23.1% higher CV than swept wings. Thus, in flapping, the 68% increase in peak FV from swept to extended posture is likely driven by the additive positive effects of S2 (58% increase) and CV as wings extend. Extended wings outperform swept wings, even after accounting for S2, in flapping flight.

During low-J flapping flight, the performance of extended wings may benefit from emarginated primary feathers. Previous research has suggested emargination reduces induced drag and increases span efficiency in gliding flight (Spedding and McArthur, 2010; Tucker, 1993, 1995). However, our broader comparative sample contrasts with Tucker's findings, because we observed that the effects of tip emargination are likely significant during take-off (low J) but not during gliding (high J). This finding may help to explain variation in wing-tip morphology among the diverse array of soaring birds. Raptors must regularly take off vertically from the ground and may thus have slotted feathers to increase CV at low J. In contrast, pelagic soarers such as albatross (with pointed wing tips) may rarely experience low-J flight because of constant marine surface winds and long, nearly horizontal take-off trajectories into a prevailing headwind, and indeed avoid flapping flight altogether during windless conditions (Shaffer et al., 2001; Weimerskirch et al., 2000). This could explain the remarkable variation in wing shape between terrestrial and pelagic soaring birds. Future work could explore this hypothesis.

During emulated gliding flight (high J), swept wings had 10.6% higher peak CV and similar peak CV:CH ratios to extended wings. These swept wings had higher CV than extended wings, but due to reduction in S, produced 21% less vertical aerodynamic force. Peak FV in gliding is thus primarily influenced by the competing effects of reduced S and increased CV exhibited by swept wings.

In the present study, swept wings during gliding appear to behave like the delta wings of aircraft. Previous work has shown that delta wings can produce lift at post-stall attack angles using vortex lift (Er-El and Yitzhak, 1988; Polhamus, 1966). Vortex lift is caused by flow separation at the leading edge of the wing, and is therefore commonly referred to as a ‘leading-edge vortex’ (LEV). This flow forms a distinct vortex on the top of the wing which runs parallel to the leading edge, increasing lift in a non-linear fashion. In our experiment, the average critical attack angle (peak CV) during gliding was α=32 deg for swept wings and α=28 deg for extended wings. During flapping, however, both swept and extended wings had high average critical attack angles of α=48 deg and α=45 deg, respectively. Future research could explore this hypothesis to better understand the aerodynamic mechanism behind increased swept-wing CV during gliding flight.

Overall, our results were contrary to our two initial hypotheses and surprising for both extremes of advance ratio (J). Usherwood and Ellington (2002b) show that the aerodynamics of small- and medium-sized revolving wings (J=0; Re=1100 to 26,000) are relatively insensitive to variations in wing morphology and AR. This is the primary evidence that led us to develop hypothesis H1. However, close examination of their data indicates our results are consistent for revolving wings at moderate angles of attack (10 deg<α<30 deg), given that extended wings exhibited higher AR than swept wings (Table 1). For example, at α=20 deg, their model hawkmoth wing with AR=15.8 generated 43% higher CV than their model quail wing with AR=4.53, while CH was generally similar for each wing. This implies that the CV:CH ratio was also greater for the wing of higher AR (Usherwood and Ellington, 2002b, see their fig. 4C,D). Their results show that wings with 4.5<AR<15.8 produce indistinguishable maximum CV between 40 deg<α<60 deg, whereas the extended raptor wings in our study continued to exhibit higher CV and CV:CH ratios up to α=50 deg (Figs 3 and 4). Also, over the relevant range of attack angles, we observed a relatively greater effect for a given AR compared with Usherwood and Ellington (2002b). The range of AR tested by Usherwood and Ellington (2002b) varied by 3.5× whereas AR in our study varied by 1.4×. We thus conclude that extended wings outperform swept wings in emulated flapping flight when J=0, but future efforts should seek to test the relative contribution of feather emargination versus AR.

The more dramatic differences we report between wing conditions compared with the effects of AR upon performance in Usherwood and Ellington (2002b) may be due to a variety of other explanatory variables. Wings in our sample experienced 370,000<Re<1,290,000, which is above the critical Re of 200,000 where the boundary layer flow transitions from laminar to turbulent (Vogel, 1996). In contrast, Usherwood and Ellington (2002b) tested wings far smaller than those in our experiment, with a maximum Re of 26,000. This change in flow regime likely affects force production. In addition to changing AR as birds sweep back their wings, camber (cross-sectional profile), washout (spanwise twist), leading-edge angle and the magnitude of primary feather emargination change (Tucker, 1987; Withers, 1981). Heers and colleagues (2011) showed that wing porosity (herein called feather emargination) was associated with low lift coefficients and low lift:drag ratios. In our present study, extended wings exhibited greater feather emargination with less feather overlap than swept wings (Table 1). These changes in morphology could affect local flow conditions and increase span efficiency (Henningsson et al., 2014; Spedding and McArthur, 2010; Tucker, 1987, 1993, 1995). At low α, average swept wing CH values were nearly double the extended wing values, further highlighting the potential benefits of emargination at low J.

Previous studies of gliding wings (J=∞) show that changes in AR and sweep can influence aerodynamic forces (Lentink et al., 2007; Pennycuick, 1968; Tucker and Parrott, 1970). Lentink and colleagues (2007) in a study of swift wings (Apodidae), in which feathers do not exhibit significant emargination, showed that the lift coefficient was reduced as wings became increasingly swept during gliding. Our results show the opposite trend in raptors. The wings in our sample varied from 1.7<AR<5.0 and exhibited changes in sweep between 34 and 81 deg (Table 1), and, although not a statistically significant difference, swept wings had 10.6% higher CV when J=∞. Additionally, our results indicate almost no difference in peak CV:CH between swept and extended wings during emulated gliding flight. A hypothesis for future comparative study is that these differences among species are due to feather emargination.

Birds generally fully extend their wings during mid-downstroke, and most sweep their wings back during upstroke (Rayner, 1988; Tobalske, 2007). In free-flying thrush nightingales (Luscinia luscinia), the upstroke has been shown to become more aerodynamically active as flight speed increases (Hedenstrom et al., 2006; Spedding et al., 2003) and many species exhibit wing-tip reversal or hand-wing supination in which lift can be produced at very low J (Brown, 1963; Crandell and Tobalske, 2011, 2015; Tobalske and Dial, 1996), but it is generally thought of as ‘recovery stroke’ between successive downstrokes. It is hypothesized that birds may therefore be sweeping back their wings to reduce drag during the upstroke (Rayner, 1988; Tobalske, 2001). Our results provide additional indirect support for this hypothesis, as swept wings reduced horizontal (i.e. drag) forces 69% during flapping compared with extended wings.

For gliding, our results indicate there is a broad envelope of aerodynamic efficiency available (i.e. CV:CH). As CV:CH changes very little as birds sweep their wings, gliding birds are likely able to modulate S without affecting their glide angle by increasing speed during swept-wing flight. This may allow them flexibility when choosing flight speeds to meet environmental demands, such as when gliding between or within thermals. In the present study, wing sweep reduced S 26.6±10.3% on average. As S and aerodynamic forces scale linearly, it is surprising that FV does not decrease accordingly with S. As S decreases, FV decreases by 20.9%. The increase in CV that occurs with increasing wing sweep during gliding may provide raptors with a subtle mechanism to alter the magnitude of total absolute aerodynamic forces, while modulating α changes the relationship between vertical and horizontal forces.

It is important to note that living birds constantly morph their wings in ways that remain difficult to measure and understanding the precise mechanisms responsible for changes in aerodynamic performance remains challenging. Our propeller and wind tunnel models do not fully represent the complexity of what actually occurs during flapping and gliding flight (Bilo, 1971; Tobalske, 2007).

Conclusions

This experiment shows that wing sweep does not significantly influence CV:CH during modeled gliding flight (high J) but does have a significant effect on modeled flapping flight such as take-off and landing (low J). Additionally, CV is higher in swept wings than in extended wings during gliding flight, which leads us to speculate that local flow conditions are affected by wing shape. The poor performance of swept wings during spinning offers an explanation for the seemingly universal use of a fully extended wing posture during downstroke in flapping flight in birds (Tobalske and Dial, 1996; Tobalske et al., 2003a). We hypothesize that the relatively low CV and high CH values observed for flexed wings during spinning were the result of unfavorable patterns of flow; for example, preventing the formation of a LEV (Birch et al., 2004; Ellington et al., 1996; Wang et al., 2004) at low α, and perhaps causing separation of flow (stall) at higher α. In contrast, flexed wings performed better in terms of FV per unit area in gliding, questioning previous hypotheses regarding the functional significance of emarginated primaries as adaptations for efficiency during high-J flight. Future flow-visualization studies would be useful in testing these ideas.

Acknowledgements

We thank Andrew Biewener for use of the wind tunnel and force plate at the Concord Field Station, and Natalie Wright, Ondi Crino, Brandon Jackson, Heather Labbe and Pat Little for their help and advice. Two anonymous reviewers provided insightful suggestions that helped us revise the manuscript. Finally, we thank Steven Vogel, who was an extraordinary mentor, a limitless source of brilliant ideas and wit, and remains an inspiration in our hearts and minds.

This research was supported by National Science Foundation grants GRFP DGE-1313190 to B.K.v.O. and IOS-0923606, IOS-0919799 and CMMI 1234747 to B.W.T. Undergraduate research support to E.A.M. was provided by the Herchel Smith Harvard Research Award.

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